Described by Milton Friedman as "the greatest social scientist who has lived and worked in the last half-century", Gary Becker, who has died aged 83, carried out research that traversed at least a dozen different areas of economics, from black markets to racial discrimination, from crime and punishment to human capital. His pioneering of rational choice theory – the concept that individuals will pursue the most cost-effective means to achieve their intended outcome – extended the boundaries of economics, and made the discipline relevant to a wide range of human activities. Becker continued to be heavily involved in economic policy discussions right up to his death – through speaking engagements, columns and his excellent blog.

Becker was born in Pottsville, Pennsylvania, one of four children of Anna (nee Siskind) and Louis Becker. In the mid-1930s, the family moved to Brooklyn, New York, where Becker went to school. He studied mathematics at Princeton University in 1951, and completed his PhD at the University of Chicago in 1955, working closely with Friedman. Friedman reignited in Becker an interest in economics that had faded at university, by emphasising that "economics was not a game played by academics, but a tool to analyse the real world".

After three years as an assistant professor at Chicago, Becker taught at Columbia University, New York, between 1957 and 1969, during which time he received the John Bates Clark medal awarded by the American Economic Association. He returned to Chicago in 1970, becoming professor of economics and sociology at the university and the Booth School of Business.

Becker challenged the idea that economic analysis should be restricted to markets. His efforts to move economic analysis to non-market subjects such as racial discrimination, families, organ donation and immigration were initially dismissed by both economists and social scientists, and much of his research proved highly controversial.

One of his most interesting areas of study was into the economic incentives of crime (an idea that occurred to him as he considered parking illegally). He calculated that he was unlikely to be caught, and that the fine for being caught was not great enough to be a deterrent. He surmised that others might make the same calculation. This analysis has been the victim of straw-man arguments claiming that Becker believed crime was simply a matter of economic incentives. Becker always acknowledged the "human" element in the commission of crime (that most people operate under high moral constraints) and simply argued that incentives had a significant effect on our decisions and actions.

The economic incentives driving family life were another controversial, but important, area that Becker investigated. His work on the effects of education and the empowerment of women upon marriage, divorce and fertility rates culminated in A Treatise on the Family (1981).

Becker was among the first economists to discuss the economic consequences of racial discrimination. He argued that discrimination against ethnic minorities could have real and significant negative economic effects on the discriminator, through higher costs. However, he also accepted that free competition alone would not eradicate discrimination.

In recent years, it was Becker's arguments on the benefits of a free market in human organs that proved most controversial. He and his co-writer, Julio Jorge Elias, put a price on human body parts, and posited that this would help increase the number of organ donations.

Becker won the Nobel prize for economic sciences in 1992 for his work in "extending microeconomic analysis to a range of human activity, including non-market behaviour". He received the US national medal of science in 2000 and the presidential medal of freedom in 2007.

One of his theories with most resonance for the UK springs from his work on immigration. Presenting the Hayek memorial lecture at the Institute of Economic Affairs in London in 2010, Becker laid out an alternative to the nationalistic posturing that is often part of the immigration debate. Accepting that a policy of open borders was impossible, given the existence of welfare states, he argued for a market-based approach to immigration that would allow migrants to pay a fee for entry. This would be supported by a system of loans to allow low-income migrants to move to the UK. It was the sort of radical alternative that Becker was willing and able to offer in a number of policy areas.

If there is one economist who can legitimately be called a giant of the discipline upon whose shoulders future generations will stand, Becker, with his trailblazing application of economics to aspects of everyday life, is a candidate for that title. He changed the nature of economics and made it relevant to entirely new spheres of human life and interaction. It shows his impact that his methods of economic analysis – derided when he introduced them – have now become the tools used by the very best researchers across criminology, sociology and other social sciences.

In 1954, he married Doria Slote. She died in 1969. He is survived by his second wife, Guity Nashat, whom he married in 1980; by two daughters, Catherine and Judy, from his first marriage; and by two grandchildren.

• Gary Stanley Becker, economist, born 2 December 1930; died 3 May 2014